Add memoization to fibonacci and making_change for performance improvement

Author: RahwaZeslusHaile

Sprint-2/improve_with_caches/fibonacci/fibonacci.py

@@ -1,4 +1,14 @@
+cache = {}
+
+
 def fibonacci(n):
+    if n in cache:
+        return cache[n]
+    
     if n <= 1:
-        return n
-    return fibonacci(n - 1) + fibonacci(n - 2)
+        result = n
+    else:
+        result = fibonacci(n - 1) + fibonacci(n - 2)
+    
+    cache[n] = result
+    return result

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,32 +1,33 @@
 from typing import List
 
 
+cache = {}
+coins = [200, 100, 50, 20, 10, 5, 2, 1]
+
+
 def ways_to_make_change(total: int) -> int:
-    """
-    Given access to coins with the values 1, 2, 5, 10, 20, 50, 100, 200, returns a count of all of the ways to make the passed total value.
 
-    For instance, there are two ways to make a value of 3: with 3x 1 coins, or with 1x 1 coin and 1x 2 coin.
-    """
-    return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1])
+    cache.clear()
+    return ways_to_make_change_helper(total, 0)
 
 
-def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
-    """
-    Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
-    """
-    if total == 0 or len(coins) == 0:
+def ways_to_make_change_helper(total: int, coin_index: int) -> int:
+    key = (total, coin_index)
+    if key in cache:
+        return cache[key]
+    
+    if total == 0:
+        return 1
+    if coin_index >= len(coins) or total < 0:
         return 0
 
     ways = 0
-    for coin_index in range(len(coins)):
-        coin = coins[coin_index]
-        count_of_coin = 1
-        while coin * count_of_coin <= total:
-            total_from_coins = coin * count_of_coin
-            if total_from_coins == total:
-                ways += 1
-            else:
-                intermediate = ways_to_make_change_helper(total - total_from_coins, coins=coins[coin_index+1:])
-                ways += intermediate
-            count_of_coin += 1
+    coin = coins[coin_index]
+    count_of_coin = 0
+    
+    while coin * count_of_coin <= total:
+        ways += ways_to_make_change_helper(total - (coin * count_of_coin), coin_index + 1)
+        count_of_coin += 1
+    
+    cache[key] = ways
     return ways